Multiplier circuit - analytical expression

[nicrip]

I have been assigned a task that I have found to be very difficult - to try and develop an alaytical (mathematical) expression for the output voltage with respect to time of the cockroft-walton voltage doubler shown below (so that I can plot the transient response), when the input voltage is a sinusoidal source. I was wondering if anybody would know how this could be done, or if such a expression has already been developed. The problem is that the diodes continually switch and charge the caps, but I cannot assume that the caps (C1) would charge to the peak input voltage in one cycle.

Similarly with the rectifier circuit below (assume the resistor is replaced by a capacitor), how would I develop a mathematical expression for the output voltage if you cannot assume that the cap voltage reaches the peak input voltage in one cycle? Would I somehow have to find the points at which the diode switches, and continually calculate the voltage on the cap as it gains voltage over several cycles of the input voltage? I appreciate any help.

 

[Proton Soup]

it's not as if there is a pretty equation. the devices are non-linear, and so simulators like SPICE solve them numerically, which takes considerably more time to solve than linear circuits.

 

[oswaler]

I understand the difficulty of developing an analytical expression for a complex circuit like the cockroft-walton voltage doubler. However, it is not impossible and has been done before. The key to developing such an expression is to consider the behavior of the circuit in each stage and then combine them to obtain the overall output voltage.

In the case of a sinusoidal input voltage, the first step would be to analyze the behavior of the diodes and capacitors in response to the changing input voltage. This can be done by applying Kirchhoff's laws and using the diode and capacitor equations. From this analysis, you can obtain the voltage across each capacitor at any given time.

Next, you would need to consider the behavior of the diodes as they switch on and off. This can be done by using the diode's characteristic equation and determining the switching points. By combining this with the voltage across each capacitor, you can obtain the overall output voltage expression as a function of time.

Similarly, for the rectifier circuit, you would need to consider the behavior of the diode and capacitor in response to the input voltage. Again, using Kirchhoff's laws and the diode and capacitor equations, you can determine the voltage across the capacitor at any given time.

I understand that this may seem like a daunting task, but with a systematic approach and proper analysis, an analytical expression for the output voltage can be obtained. It is also important to note that these expressions may be approximations and may need to be verified through simulations or experiments. I suggest consulting with a colleague or conducting further research to find similar circuits and their corresponding analytical expressions as a reference. I wish you the best of luck in your task.